2026/7/20-2026/7/24, Ludovic Goudenege 氏 (Université d'Evry-Paris Saclay)
Title: Numerical Schemes for SDEs and PDEs with Applications to Quantitative Finance
Abstract: This course introduces numerical methods for stochastic differential equations (SDEs) and partial differential equations (PDEs), with applications to quantitative finance. It presents the fundamental link between sampling stochastic models and pricing PDEs through the Feynman–Kac formula.
The course covers time discretization schemes for SDEs, tree-based and Monte Carlo methods, as well as finite difference and related methods for PDEs. Applications include European and American option pricing, high-dimensional models, and optimal stopping problems.
Finally, modern machine learning techniques are introduced as efficient tools for pricing in high dimensions, particularly when classical numerical methods become impractical. Hybrid approaches combining Monte Carlo simulation, exact integration, and learning-based methods are discussed in both Markovian and non-Markovian settings.
Place : Nishi waseda campus, Waseda University building No 51, 17th or 18th floors.
July 20 17-06 (2nd and 4th period), 17-04 (3rd period)
July 21 17-06 (2,3,4 periods)
July 22 18-06 (2,3,4 periods)
July 23 17-06 (2,3,4 periods)
July 24 17-08 (2,3,4 periods)